From the pictures and from my own experience on the two birds, the BBJ is certainly nicer, but you cannot really compare these cabins. They're in a very different price region.

The ACJ shown in your pictures is more like a corporate shuttle. Airbus is trying to sell the ACJ as an executive/VIP plane too, but they're not yet that sucessfull in that sector. As far as I know, no ACJ in VIP config comparable to the Boeing demonstrator has been built so far. The ACJ shown at the shows is actually not an Airbus demonstrator, the plane is always leased from AeroService.

The BBJ in comparision does really feature a VIP cabin, at least in the pictures above. I have already seen a number of BBJs in different configuration. Some were designed as corporate shuttles, some as VIP planes. All were very nice, of course.

Personaly, I prefer the BBJ over the ACJ, but more from an operational standpoint. The interior is always designed to the wishes of the customer, and therefore you cannot compare them.

I think that it's probably very much possible to order the interiors to both planes from the same companies, I don't think Boeing or Airbus builds or installs them. And since AFAIK all BBJs and ACJs are built with custom interiors, I think plane-wise the only difference between them is that the ACJ is a bit wider.